December 16, 2018 December 16, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. December 16, 2018 December 16, 2018 03:00 PM EST 04:00 PM EST Strategies and techniques for approaching featured GMAT topics
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51229

If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
21 Aug 2018, 19:51
Question Stats:
21% (01:21) correct 79% (01:35) wrong based on 207 sessions
HideShow timer Statistics




CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2711
Location: India
GMAT: INSIGHT
WE: Education (Education)

If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 20:56
Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Interesting question Here the question says rain on atleast three days CONSECUTIVELYi.e. Exactly three days in row Days123 or days 234 or days 345 or days 1235 or days 1345i.e. Exactly Four days Days1234 or days 2345or exactly 5 days days 12345Probability in each case = (1/2)^5 Required Probability = 8*(1/32) = 1/4 Answer: Option B A VARIATION AND A NEW QUESTIONHad the question been Probability of Rain on Atleast three days out of 5If it rains on exactly 3 days out of 5 then those 3 days can be selected in 5C3 ways and therefore Probability = \(5C3*(0.5)^3*(0.5)^2 = 5C3*(1/32)\)If it rains on exactly 4 days out of 5 then those 3 days can be selected in 5C4 ways and therefore Probability = \(5C4*(0.5)^4*(0.5)^1 = 5C4*(1/32)\)If it rains on exactly 5 days out of 5 then those 3 days can be selected in 5C5 ways and therefore Probability = \(5C5*(0.5)^5 = 5C3*(1/32)\)Total Probability of raining atleast 3 out of 5 days = (1/32)*(5C3+5C4+5C5) = 16/32 = 1/2
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Expert
Joined: 02 Aug 2009
Posts: 7108

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 20:00
Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Important not to miss ' in a row'.. At least three days means three cases... 1) 3 days in a row.. So take these three days as ONE R and other two as N So NNR.. You can place R in 3C1=3 ways 2) 4 days.....4 days in a row OR 3 days in a row and 4th day of rain separated by a non rainy day So take these three days as ONE R and nonrainy day as N and 4th day as r So rNR........ rNR, rRN, RNr,rRN 4 ways 3) 5 days in a row All 5 are one so one way Total 3+4+1=8 All possibilities=2*2*2*2*2=32 Probability=8/32=1/4 gmatnovice1122, what is wrong with your way.. Firstly you are complicating a simple way.. We use complement when we went to ease our calculations as normal scenario will have more casesIf talking of complement.. At least three days in a row means MAX two days in a row.. 1) two days.. When there are 4 days of rains....RRNRR When there are three days....RNNRR, NRNRR, ....many ways When there are 2 days....RRNNN, NRRNN..and so on 2) one day.. 4days is not possible 3 days..RNRNR 2 days ...NNRNR, and so on 3) none of the day NNNNN... One way So as you see it is more complicated, stick to normal
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
21 Aug 2018, 21:07
Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 \(5C_3(\frac{1}{2})^3(\frac{1}{2})^2\) \(= \frac{5}{16}\) , Answer must be (D)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2323

If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
21 Aug 2018, 21:30
Solution Given:• Probability of rain on any given day is 50% To find:• The probability that it will rain on at least three days in a row during a fiveday period Approach and Working: Assume that R represents rain and N represents no rain As probability of rain is 50%, each of R and N have individual probability ½. Now, at least 3 rainy days in a row can happen when • Exact 3 rain and 2 no rain: RRRNN or NRRRN or NNRRR or RRRNR or RNRRR • Exact 4 rain and 1 no rain: RRRRN or NRRRR • Exact 5 rain: RRRRR Hence, the probability = (5 + 2 + 1) x \((\frac{1}{2})^5\) = \(\frac{8}{32}\) = \(\frac{1}{4}\) Hence, the correct answer is option B. Answer: B
_________________
Register for free sessions Number Properties  Algebra Quant Workshop
Success Stories Guillermo's Success Story  Carrie's Success Story
Ace GMAT quant Articles and Question to reach Q51  Question of the week
Must Read Articles Number Properties – Even Odd  LCM GCD  Statistics1  Statistics2  Remainders1  Remainders2 Word Problems – Percentage 1  Percentage 2  Time and Work 1  Time and Work 2  Time, Speed and Distance 1  Time, Speed and Distance 2 Advanced Topics Permutation and Combination 1  Permutation and Combination 2  Permutation and Combination 3  Probability Geometry Triangles 1  Triangles 2  Triangles 3  Common Mistakes in Geometry Algebra Wavy line  Inequalities Practice Questions Number Properties 1  Number Properties 2  Algebra 1  Geometry  Prime Numbers  Absolute value equations  Sets
 '4 out of Top 5' Instructors on gmatclub  70 point improvement guarantee  www.egmat.com



eGMAT Representative
Joined: 04 Jan 2015
Posts: 2323

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
21 Aug 2018, 21:35



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
21 Aug 2018, 21:35
Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Say , symbols R=Rain , N=No rain Given \(P(R)=P(N)=\frac{1}{2}\) P(at least 3 Rainy days in a row)=P(3 rainy days in a row)+P(4 rainy days in a row)+P(5 rainy days in a row) 1) P(3 rainy days in a row)=\(5*(\frac{1}{2})^5\) RRRNR RRRNN NNRRR RNRRR NRRRN 2) P( 4 rainy days in a row)=\(2*(\frac{1}{2})^5\) RRRRN NRRRR 3) P( 5 rainy days in a row)=\((\frac{(1}{2)})^5\) RRRRR So, required probability=\(5*(\frac{1}{2})^5\)+\(2*(\frac{1}{2})^5\)+\((\frac{1}{2})^5\)=\(8*(\frac{1}{2})^5\)=\(8*\frac{1}{32}\)=\(\frac{1}{4}\) Ans. (B)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



Manager
Joined: 01 Feb 2017
Posts: 171

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
22 Aug 2018, 20:35
'Coin Flip' analogy
5 flips; what is the Probability of getting atleast three tails in a row?
Probability of 1 event= 1/2^5
Favorable events (by manual counting):
1) Three tails in a row: 5 TTTHH + TTTHT HTTTH HHTTT + THTTT 2) Four tails in a row: 2 TTTTH HTTTT
3) Five tails in a row: 1 TTTTT
Ans: 8/2^5= 8/32= 1/4 Choice B
Posted from my mobile device



Intern
Joined: 15 Aug 2012
Posts: 42

If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
11 Sep 2018, 05:26
EgmatQuantExpert wrote: Solution Given:• Probability of rain on any given day is 50% To find:• The probability that it will rain on at least three days in a row during a fiveday period Approach and Working: Assume that R represents rain and N represents no rain As probability of rain is 50%, each of R and N have individual probability ½. Now, at least 3 rainy days in a row can happen when • Exact 3 rain and 2 no rain: RRRNN or NRRRN or NNRRR or RRRNR or RNRRR • Exact 4 rain and 1 no rain: RRRRN or NRRRR • Exact 5 rain: RRRRR Hence, the probability = (5 + 2 + 1) x \((\frac{1}{2})^5\) = \(\frac{8}{32}\) = \(\frac{1}{4}\) Hence, the correct answer is option B. Answer: BHi EgmatQuantExpertFor below scenario, why do we also need to count the last two cases? That's when there are 4 rainy days. Exact 3 rain and 2 no rain: RRRNN or NRRRN or NNRRR or RRRNR or RNRRR



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4295
Location: United States (CA)

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
14 Sep 2018, 16:51
Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Let R = rain and N = no rain. To have at least three days in a row during a fiveday period, we could have: RRRNN, NRRRN, NNRRR, RRRRN, NRRRR, RNRRR, RRRNR and RRRRR. Notice that the probability of R is ½ and the probability of N is also ½. Thus, the probability of any of the scenarios above is ½ x ½ x ½ x ½ x ½ = (½)^5 = 1/32. Since we have a total of 6 scenarios, the overall probability is 8 x 1/32 = 1/4. Answer: B
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 18 Jun 2018
Posts: 4

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 14:57
Bunuel, chetan2u, @mikemcgarry,@VeritasKarishma,@niks18,@generis Can anyone please explain how do you solve this using the complement "At Least" rule? If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period? Can we solve using the opposite or negation role in which case N  3 = 2. P(it will rain on at least three days in a row) = 1  P(it will rain on at least two or fewer days in a row). P(it will rain on at least two or fewer days in a row) = Raining on any one week day = 5/32 (RNNNN,NRNNN, NNRNN,NNNRN,NNNNR) Raining on any two consecutive days in a row = 4 / 32 (RRNNN, NRRNN, NNRRN, NNNRR) 4/32 + 5/32 = 9/32 1  9/32 = 23/32 (It is not one of the answer)!



Intern
Joined: 18 Jun 2018
Posts: 4

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 15:02
ScottTargetTestPrep wrote: Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Let R = rain and N = no rain. To have at least three days in a row during a fiveday period, we could have: RRRNN, NRRRN, NNRRR, RRRRN, NRRRR, RNRRR, RRRNR and RRRRR. Notice that the probability of R is ½ and the probability of N is also ½. Thus, the probability of any of the scenarios above is ½ x ½ x ½ x ½ x ½ = (½)^5 = 1/32. Since we have a total of 6 scenarios, the overall probability is 8 x 1/32 = 1/4. Answer: B Hi ScottTargetTestPrepCan anyone please explain how do you solve this using the complement "At Least" rule? If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period? Can we solve using the opposite or negation role in which case N  3 = 2. P(it will rain on at least three days in a row) = 1  P(it will rain on at least two or fewer days in a row). P(it will rain on at least two or fewer days in a row) = Raining on any one week day = 5/32 (RNNNN,NRNNN, NNRNN,NNNRN,NNNNR) Raining on any two consecutive days in a row = 4 / 32 (RRNNN, NRRNN, NNRRN, NNNRR) 4/32 + 5/32 = 9/32 1  9/32 = 23/32 (It is not one of the answer)!



Manager
Joined: 21 Jul 2018
Posts: 56

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 15:30
It was a quite confusing one took me around 10 mins to understand the solution.
_________________
______________________________ Consider KUDOS if my post helped !!
I'd appreciate learning about the grammatical errors in my posts
Please let me know if I'm wrong somewhere



Intern
Joined: 18 Jun 2018
Posts: 4

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 15:32
parthos wrote: It was a quite confusing one took me around 10 mins to understand the solution. parthosI understand the solution but why cannot we solve it with the complement.



Manager
Joined: 21 Jul 2018
Posts: 56

Re: If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
19 Sep 2018, 15:38
alirehman4657 wrote: parthos wrote: It was a quite confusing one took me around 10 mins to understand the solution. parthosI understand the solution but why cannot we solve it with the complement. I believe the approach used by you to find solution is incorrect in this type of question and as I told you in the chat I am not expert in probability hence please contact some seniors for this. Thanks !!
_________________
______________________________ Consider KUDOS if my post helped !!
I'd appreciate learning about the grammatical errors in my posts
Please let me know if I'm wrong somewhere



Intern
Joined: 18 Jun 2018
Posts: 4

If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
20 Sep 2018, 04:32
chetan2u wrote: Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Important not to miss ' in a row'.. At least three days means three cases... 1) 3 days in a row.. So take these three days as ONE R and other two as N So NNR.. You can place R in 3C1=3 ways 2) 4 days.....4 days in a row OR 3 days in a row and 4th day of rain separated by a non rainy day So take these three days as ONE R and nonrainy day as N and 4th day as r So rNR........ rNR, rRN, RNr,rRN 4 ways 3) 5 days in a row All 5 are one so one way Total 3+4+1=8 All possibilities=2*2*2*2*2=32 Probability=8/32=1/4 what is wrong with your way.. Firstly you are complicating a simple way.. We use complement when we went to ease our calculations as normal scenario will have more casesIf talking of complement.. At least three days in a row means MAX two days in a row..(IS THE COMPLEMENT OF AT LEAST THREE DAYS IN A ROW = 1  P(MAX TWO DAYS)???) 1) two days.. When there are 4 days of rains....RRNRR When there are three days....RNNRR, NRNRR, ....many ways When there are 2 days....RRNNN, NRRNN..and so on 2) one day.. 4days is not possible 3 days..RNRNR 2 days ...NNRNR, and so on 3) none of the day NNNNN... One way So as you see it is more complicated, stick to normal chetan2uGMATinsightThanks for your respond. I appreciate the feedback. I was confused because when reviewing probabilities, you are thought that when you have the words "AT LEAST" to automatically use the complement. As a result, that is the method I followed. Also, wouldn't the complement of P(Rain on AT LEAST three days in a row) be 1  P(Rain on AT LEAST two or fewer days in a row. and NOT as you stated above..so it would be RRNNN,NRRNN, etc? Is my understanding of complements wrong? In the past I solved a problem related to selecting cards out of a 52 card deck, that stated P (at least the third draw). The complement of this was used 1  p(two or fewer draws). Thanks again for helping clarify this.



Math Expert
Joined: 02 Aug 2009
Posts: 7108

If the probability of rain on any given day is 50%, what is the probab
[#permalink]
Show Tags
20 Sep 2018, 04:45
gmatnovice1122 wrote: chetan2u wrote: Bunuel wrote: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least three days in a row during a fiveday period?
A. 3/32 B. 1/4 C. 9/32 D. 5/16 E. 1/2 Important not to miss ' in a row'.. At least three days means three cases... 1) 3 days in a row.. So take these three days as ONE R and other two as N So NNR.. You can place R in 3C1=3 ways 2) 4 days.....4 days in a row OR 3 days in a row and 4th day of rain separated by a non rainy day So take these three days as ONE R and nonrainy day as N and 4th day as r So rNR........ rNR, rRN, RNr,rRN 4 ways 3) 5 days in a row All 5 are one so one way Total 3+4+1=8 All possibilities=2*2*2*2*2=32 Probability=8/32=1/4 what is wrong with your way.. Firstly you are complicating a simple way.. We use complement when we went to ease our calculations as normal scenario will have more casesIf talking of complement.. At least three days in a row means MAX two days in a row..(IS THE COMPLEMENT OF AT LEAST THREE DAYS IN A ROW = 1  P(MAX TWO DAYS)???) 1) two days.. When there are 4 days of rains....RRNRR When there are three days....RNNRR, NRNRR, ....many ways When there are 2 days....RRNNN, NRRNN..and so on 2) one day.. 4days is not possible 3 days..RNRNR 2 days ...NNRNR, and so on 3) none of the day NNNNN... One way So as you see it is more complicated, stick to normal chetan2uGMATinsightThanks for your respond. I appreciate the feedback. I was confused because when reviewing probabilities, you are thought that when you have the words "AT LEAST" to automatically use the complement. As a result, that is the method I followed. Also, wouldn't the complement of P(Rain on AT LEAST three days in a row) be 1  P(Rain on AT LEAST two or fewer days in a row. and NOT as you stated above..so it would be RRNNN,NRRNN, etc? Is my understanding of complements wrong? In the past I solved a problem related to selecting cards out of a 52 card deck, that stated P (at least the third draw). The complement of this was used 1  p(two or fewer draws). Thanks again for helping clarify this. Hi.. At least 3 days means on 3 days, 4 days and 5 days.. So complement will be 1(no days, 1 days and 2 days) The moment you do at least 2 days, it itself will be contain at least 3 days or at least 4 days.. So if you do 1(atleast 2 days or few days) means 1(probability of rain on 2 days, 3 days , 4 days and 5 days)
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor




If the probability of rain on any given day is 50%, what is the probab &nbs
[#permalink]
20 Sep 2018, 04:45






